Property:Abstract
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M
We consider the problem of planning motions in observations space, based on learned models of the dynamics that associate to each action a diffeomorphism of the observations domain. For an arbitrary set of diffeomorphisms, this problem must be formulated as a generic search problem. We adapt established algorithms of the graph search family. In this scenario, node expansion is very costly, as each node in the graph is associated to an uncertain diffeomorphism and corresponding predicted observations. We describe several improvements that ameliorate performance: the introduction of better image similarities to use as heuristics; a method to reduce the number of expanded nodes by preliminarily identifying redundant plans; and a method to pre-compute composite actions that make the search efficient in all directions. +
A
We consider the problem of purely visual pose stabilization (also known as servoing) of a second-order rigid- body system with six degrees of freedom: how to choose forces and torques, based on the current view and a memorized goal image, to steer the pose towards a desired one. Emphasis has been given to the bio-plausibility of the computation, in the sense that the control laws could be in principle implemented on the neural substrate of simple insects. We show that stabilizing laws can be realized by bilinear/quadratic operations on the visual input. This particular computational structure has several numerically favorable characteristics (sparse, local, and parallel), and thus permits an efficient engineering implementation. We show results of the control law tested on an indoor helicopter platform. +
We consider the problem of purely visual pose stabilization of a second-order rigid-body system: how to choose forces and torques, based on the visual input alone, such that the view converges to a memorized goal image. Emphasis has been given to the bio-plausibility of the computation, in the sense that the control laws could be in principle implemented on the neural substrate of simple insects. We show that stabilizing laws can be realized by bilinear/quadratic operations on the visual input. Moreover, the control laws can be ``bootstrapped'' (learned unsupervisedly) from experience, which further substantiate the bio-plausibility of such computation. +
S
We consider the problem of reasoning about networked and layered control systems using assume-guarantee specifications. As these systems are formed by the interconnection of components that operate under various clocks, we introduce a new logic, Multiclock Logic (MCL), to be able to express the requirements of components form the point of view of their local clocks. Specifying components locally promotes independent design and component reuse. We carry out a contract-based analysis of a control system implemented via two control algorithms (model predictive control and feedback linearization) running on their own processors and clocks. Then we implement each of the contracts to build a system. The system performs as desired when the requirements derived from our system-level analysis are respected. Violating the constraints required by the contract-based analysis of the system leads to error. +
T
We consider the problem of synthesizing hier- archical controllers for discrete-time switched affine systems subject to exogenous disturbances that guarantee that the trajectories of the system satisfy a high-level specification expressed as a linear temporal logic formula. Our method builds upon recent results on temporal logic planning and embedded controller synthesis. First, the control problem is lifted to a discrete level by constructing a finite transition system that abstracts the behavior of the underlying switched system. At the discrete level, we recast the problem as a two player temporal logic game by treating the environment driven switches as adversaries. The solution strategy for the game (i.e. the discrete plan) is then implemented at the continuous level by solving finite-horizon optimal control problems that establish reachability between discrete states and that compensate the effects of continuous disturbances. We also extend the earlier work by making efficient use of propositions in the temporal logic formula to drive the abstraction procedure and to facilitate the computation of continuous input at implementation time.
An aircraft fuel system example is formulated; and solved using the proposed method. This sample problem demonstrates the applicability of the abstraction procedure and correct-by-construction controllers to regulate the fuel levels in multiple tanks during interesting operations like aerial refueling. +
D
We consider the problem of synthesizing control protocols for smart camera networks where the goal is to guarantee that certain linear temporal logic (LTL) specifications related to a given surveillance task are met. We first present a centralized control architecture for assigning pan-tilt-zoom (PTZ) cameras to targets so that the specification is met for any admissible behavior of the targets. Then, in order to alleviate the computational complexity associated with LTL synthesis and to enable implementation of local control protocols on individual PTZ cameras, we propose a distributed synthe- sis methodology. The main idea is to decompose the global specification into local specifications for each PTZ camera. A thorough design example is presented to illustrate the steps of the proposed procedure. +
H
We consider the problem of synthesizing robot controllers to realize a task that unpredictably changes with time. Tasks are formally expressed in the GR(1) fragment of temporal logic, in which some of the variables are set by an adversary. The task changes by the addition or removal of goals, which occurs online (i.e., at run-time). We present an algorithm for mending control strategies to realize tasks after the addition of goals, while avoiding global re-synthesis of the strategy. Experiments are presented for a planar surveillance task in which new regions of interest are incrementally added. Run-times are empirically shown to be extremely favorable compared to re-synthesizing from scratch. We also present an algorithm for mending control strategies for the removal of goals. While in this setting the original strategy is still feasible (as we prove), our algorithm provides a more satisfying solution by âtightening loose ends.â Both algorithms are shown to yield so-called reach annotations, and thus the control strategies are easily amenable to other algorithms concerning incremental synthesis, e.g., as in previous work by the authors for robot navigation in uncertain environments. +
E
We define a notion of controllability for mechanical systems which determines
the configurations which are accessible from a given configuration. We
derive sufficient conditions for this notion of controllability in terms of
the given inputs, their Lie brackets, and their covariant derivatives. +
R
We define the real time trajectory generation problem to be how to generate,
possibly with some delay, a full state space and input trajectory in real
time from an output trajectory that is given online, while allowing a
tradeoff between stability and performance. We
propose two algorithms that solve the real time trajectory generation
problem for flat systems with zero dynamics, and discuss some interesting
properties. We explicitly address the tradeoff between stability and
performance. The algorithms are validated in simulations and experiments
with a thrust vectored ducted fan aircraft. +
A
A two-state ribosome and protein model can robustly capture the chemical reaction dynamics of gene expression +
We derive phenomenological models of gene expression from a mechanistic description of chemical reactions using an automated model reduction method. Using this method, we get analytical descriptions and computational performance guarantees to compare the reduced dynamics with the full models. We develop a new two-state model with the dynamics of the available free ribosomes in the system and the protein concentration. We show that this new two-state model captures the detailed mass-action kinetics of the chemical reaction network under various biologically plausible conditions on model parameters. On comparing the performance of this model with the commonly used mRNA transcript-protein dynamical model for gene expression, we analytically show that the free ribosome and protein model has superior error and robustness performance. +
D
We describe a method for discrete representation of continuous functions and show how
this may be used for typical computations in nonlinear control desi gn. The method
involves representing functions by their values and finitely many derivatives at discrete
set of points on the domain. We propose a grid structure based on a hierarchy of
rectangular boxes that provides flexibility in placing grid points densely in some regions
and sparsely in the other. The grids possess enough structure to facilitate easy
interpolation schemes based on piecewise polynomials. We illustrate the method using a
simple example where we compute the feedback linearizing output of a system. +
C
Coarse analysis of multiscale systems: diffuser flows, charged particle motion, and connections to averaging theory +
We describe a technique for the efficient computation of the dominant-scale dynamics of a fluid
system when only a high-fidelity simulation is available. Such a technique is desirable when governing equations for the dominant scales are unavailable, when model reduction is impractical, or
when the original high-fidelity computation is expensive. We adopt the coarse analysis framework
proposed by I. G. Kevrekidis (Comm. Math. Sci. 2003), where a computational superstructure is
designed to use short-time, high-fidelity simulations to extract the dominant features for a multi-
scale system. We apply this technique to compute the dominant features of the compressible flow
through a planar diffuser. We apply the proper orthogonal decomposition to classify the dominant
and subdominant scales of diffuser flows. We derive a suitable coarse pro jective Adams-Bashforth
time integration routine and apply it to compute averaged diffuser flows. The results include accu-
rate tracking of the dominant-scale dynamics for a range of parameter values for the computational
superstructure. These results demonstrate that coarse analysis methods are useful for solving fluid
flow problems of a multiscale nature.
<p>
In order to elucidate the behavior of coarse analysis techniques, we make comparisons to averaging
theory. To this end, we derive governing equations for the average motion of charged particles in
a magnetic field in a number of different settings. First, we apply a novel procedure, inspired by WKB theory and Whitham averaging, to average the variational principle. The resulting equations
are equivalent to the guiding center equations for charged particle motion; this marks an instance
where averaging and variational principles commute. Secondly, we apply Lagrangian averaging
techniques, previously applied in fluid mechanics, to derive averaged equations. Making comparisons to the WKB/Whitham-style derivation allows for the necessary closure of the Lagrangian
averaging formulation. We also discuss the Hamiltonian setting and show that averaged Hamiltonian systems may be derivable using concepts from coarse analysis. Finally, we apply a prototypical
coarse analysis procedure to the system of charged particles and generate tra jectories that resemble
guiding center tra jectories. We make connections to perturbation theory to derive guidelines for the
design of coarse analysis techniques and comment on the prototypical coarse analysis application.
L
We describe the interaction of a rigid body and its incompressible fluid environment
with reduced Euler-Lagrange equations on the appropriate Cartesian product manifold. We
propose a modification to the planar form of these equations to accomodate control inputs
consistent with a model for carangiform swimming. Initial Lie algebraic analysis of the
resulting control system suggests its usefulness in predicting efficacious gaits for
piscimimetic robots. +
E
We describe the structure of connected graphs with the minimum and maximum average distance, radius, diameter, betweenness centrality, efficiency and resistance distance, given their order and size. We find tight bounds on these graph qualities for any arbitrary number of nodes and edges and analytically derive the form and properties of such networks. +
N
We describe the structure of the graphs with the smallest average distance and the largest average clustering given their order and size. There is usually a unique graph with the largest average clustering, which at the same time has the smallest possible average distance. In contrast, there are many graphs with the same minimum average distance, ignoring their average clustering. The form of these graphs is shown with analytical arguments. Finally, we measure the sensitivity to rewiring of this architecture with respect to the clustering coefficient, and we devise a method to make these networks more robust with respect to vertex removal. +
S
We develop a framework for control protocol syn- thesis for a platoon of autonomous vehicles subject to temporal logic specifications. We describe the desired behavior of the platoon in a set of linear temporal logic formulas, such as collision avoidance, close spacing or comfortability. The problem of decomposing a global specification for the platoon into distributed specification for each pair of adjacent vehicles is hard to solve. We use the invariant specifications to tackle this problem and the decomposition is proved to be scalable.. Based on the specifications in Assumption/Guarantee form, we can construct a two-player game (between the vehicle and its closest leader) locally to automatically synthesize a controller protocol for each vehicle. Simulation example for a distributed vehicles control problem is also shown. +
O
Optimal Control of Non-deterministic Systems for a Computationally Efficient Fragment of Temporal Logic +
We develop a framework for optimal control policy synthesis for non-deterministic transition systems subject to temporal logic specifications. We use a fragment of temporal logic to specify tasks such as safe navigation, response to the environment, persistence, and surveillance. By restricting specifications to this fragment, we avoid a potentially doubly-exponential automaton construction. We compute feasible con- trol policies for non-deterministic transition systems in time polynomial in the size of the system and specification. We also compute optimal control policies for average, minimax (bottleneck), and average cost-per-task-cycle cost functions. We highlight several interesting cases when these can be computed in time polynomial in the size of the system and specification. Additionally, we make connections between computing optimal control policies for an average cost-per-task-cycle cost function and the generalized traveling salesman problem. We give simulation results for motion planning problems. +
A
We develop a method for the control of discrete-time nonlinear systems
subject to temporal logic specifications. Our approach uses a coarse
abstraction of the system and an automaton representing the temporal logic
specification to guide the search for a feasible trajectory. This decomposes
the search for a feasible trajectory into a series of constrained
reachability problems. Thus, one can create controllers for any system for
which techniques exist to compute (approximate) solutions to constrained
reachability problems. Representative techniques include sampling-based
methods for motion planning, reachable set computations for linear systems,
and graph search for finite discrete systems. Our approach avoids the
expensive computation of a discrete abstraction, and its implementation is
amenable to parallel computing. We demonstrate our approach with numerical
experiments on temporal logic motion planning problems with high-dimensional
(10+ states) continuous systems. +
We develop a system for implementing “packet-based” intercellular communication in an engineered bacterial population via conjugation. Our system uses gRNA-based identification markers that allow messages to be addressed to specific strains via Cas9-mediated cleavage of messages sent to the wrong recipient, which we show reduces plasmid transfer by four orders of magnitude. Integrase-mediated editing of the address on the message plasmid allows cells to dynamically update the message’s recipients in vivo. As a proof-of-concept demonstration of our system, we propose a linear path scheme that would propagate a message sequentially through the strains of a population in a defined order. +
C
We develop the study of primitives of human motion, which we
refer to as movemes. The idea is to understand human motion by
decomposing it into a sequence of elementary building blocks that belong
to a known alphabet of dynamical systems. Where do these dynamic
primitives come from in practice? How can we construct an alphabet of
movemes from human data? In this paper we address these issues. We define
conditions under which collections of signals are well-posed according to
a dynamical model class M and thus can generate movemes. Using examples
from human drawing data, we show that the definition of well-posedness
can be applied in practice so to establish if sets of actions, reviewed as
signals in time, can define movemes. +
